Physics, 19.11.2020 22:00 maxB0846

A force F is applied to a cylindrical steel cable of diameter 3.5 mm and length 10.0 m. Determine the value of F if the change in length of the cable is 7.8 mm. Ysteel = 20 x 10^10 N/m2

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Answer from: dylancasebere

The value of force (F) if the change in length of the cable is 7.8 mm is 1500.89 N

The value of the force can be determined by using the young modulus equation that shows the relation between the tensile of the steel cable when the force is applied.

$\mathbf{\gamma = \dfrac{F/A}{\Delta L/L}}$

$\mathbf{\gamma = \dfrac{F} {A }\times \dfrac{L}{\Delta L} }$

Making the force the subject of the formula and replacing the values, we have:

$\mathbf{F =\dfrac{A \times \gamma \times \Delta L }{L} }$

$\mathbf{F =\dfrac{ \pi \times (3.5 \times 10^{-3}) \times ( 20 \times 10^{10} \ N/m^2 ) \times (7.8 \times 10^{-3}) }{4 \times 10} }$

$\mathbf{F =1500.89 \ N }$

Therefore, we can conclude that the value of force (F) if the change in length of the cable is 7.8 mm is 1500.89 N

Learn more about young modulus here:

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Answer from: anenee1

Explanation:

Mathematicians seek and use patterns[8][9] to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements.[10] Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.[11]

Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences.

Answer from: Quest

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Answer from: Quest

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A force F is applied to a cylindrical steel cable of diameter 3.5 mm and length 10.0 m. Determine th...